For the purposes of understanding the present invention, it is useful to consider a representation of the total optical E-field E(t) as a vector confined to a plane and emanating from a fixed origin, where the length of the vector gives the amplitude of the E-field at any instant (t), and the direction of the vector gives the phase of the field at any instant (t). Within this construction, we consider two basis sets. The first basis set is a Cartesian coordinate system centered on the E-field origin. In this Cartesian representation, the total E-field E(t) is decomposed along the orthogonal Real (Re) and Imaginary (Im), or, equivalently, In-phase (I) and Quadrature (Q), directions. The second basis set is a polar coordinate system, again sharing its origin with that of the E-field vector. In this polar representation, the E-field is decomposed into vector length (S) and phase angle (φ) relative to the Re-direction. These two basis sets are related by a non-linear transformation, in a manner well known in the art. In each of these representations, the time-sequence of loci of the end-point of the E-field vector may be referred to as a trajectory of the E-field.
In the optical communications space, various techniques are used to synthesize an optical communications signal for transmission. A popular technique utilizes a laser 2 coupled to an external Electrical-to-Optical (E/O) converter 4, as shown in FIG. 1a. The laser 2 generates a narrow-band continuous wave (CW) optical carrier signal 6 having a desired wavelength. The E/O converter 4 operates to modulate the amplitude and/or phase of the carrier signal 6 to generate the optical communications signal 8 based on one or more drive signals S(t) generated by a driver circuit 10 based on an input data signal x(t).
In the arrangement illustrated in FIG. 1a, the E/O converter 4 is provided by a well known Mach-Zehnder (MZ) interferometer. Other types of E/O converters may be used, depending on the desired type of modulation. For example, an electro-absorptive E/O converter (EAM) or a variable optical attenuator (VOA) may be used for amplitude modulation, whereas phase shifters are well known for implementing phase modulation schemes. In each case, the driver circuit 10 generates the drive signals S(t), primarily by scaling the input data signal x(t) to satisfy the voltage and current requirements of the E/O converter 4. In some cases, the input data signal x(t) is encoded in accordance with a desired modulation scheme (e.g. for quadrature encoding), and the resulting encoded data signal scaled to satisfy the voltage and current requirements of the E/O converter 4. The format of the drive signal S(t) output from the driver circuit 10 is principally governed by the desired modulation scheme, and will typically take the form of a baseband (i.e., binary, direct current) signal; a coded (e.g. quadrature encoded) signal; or a modulated electrical (e.g. radio frequency) carrier signal. In addition, each drive signal may also be generated in the form of a differential signal pair ±S(t), which provides certain advantages known in the art. In all cases, the drive signals S(t) are directly modeled on the input data signal x(t), and represent the data to be modulated onto the CW carrier 6. This is true even where an encoding scheme, such as quadrature encoding, is used.
For example, FIGS. 1a and 1b illustrate a conventional transmitter in which an input data signal x(t) is transmitted using the well known On-Off Keying (OOK) modulation scheme. As may be seen in FIG. 1a, the driver 10 scales the input data signal x(t) to produce a differential pair of bi-state (that is two-level) baseband drive signals ±S(t). The baseband drive signal pair ±S(t) is then used to drive excursions of the E/O converter's (sinusoidal) amplitude response between maximum and minimum transmittance, as may be seen in FIG. 1b. This operation yields an amplitude-modulated optical communications signal 8 having an optical E-field EO(t) which exhibits excursions of amplitude between two states reflecting the binary values of each bit of the input data signal x(t), as shown in FIG. 1c, in which the optical E-field EO(t) is represented in the complex Re/Im plane. As may be seen in FIG. 1c, amplitude modulation of the CW carrier 6 in the above manner results in excursions of the optical E-field EO(t) between loci clustered about two points on the real (Re) axis. Ideally, all of the E-field loci will be located on the real (Re) axis. However, in practice the optical E-field EO(t) will also exhibit excursions in the imaginary (Im) direction due to phase chirp resulting from coupling of phase and amplitude responses of all real electro-optical devices.
FIG. 1d illustrates an arrangement in which the input data signal x(t) is encoded by an encoder block 12 prior to scaling. Various encoding schemes are known in the art. For example, U.S. Pat. No. 6,522,439 (Price et al), teaches an arrangement in which the input data signal x(t) is split into a pair of parallel In-phase (I) and Quadrature (O) signal components (i.e. the sine and cosine of the data signal x(t)), which are then modulated onto an electrical (RF) carrier and scaled to yield a corresponding pair of drive signals SI(t) and SQ(t). U.S. Pat. No. 5,892,858 (Vaziri et al) teaches another arrangement in which the input data signal x(t) is sampled to generate a duo-binary encoded signal, which is then scaled to generate the drive signal. It is also known to quadrature encode the input data signal x(t) prior to scaling. In this case, the input data signal x(t) is divided into successive 2-bit symbols. The stream of symbols is then supplied to the driver circuit 10, which outputs a quad-state (i.e. four-level) drive signal S(t). Driving the phase response of the E/O converter 4 with the quadrature-encoded quad-state drive signal S(t) yields a communications signal 8 having an optical E-field EO(t) which exhibits phase excursions between four discrete states reflecting the binary values of each 2-bit symbol. This is illustrated in FIG. 1e, in which the optical E-field EO(t) is represented in the complex Re/Im plane. As may be seen in FIG. 1e, quadrature phase shift modulation of the CW carrier 6 in the above manner results in excursions of the E-field E(t) between loci clustered about four points which are roughly symmetrically distributed about the origin. Here again, scatter of the E-field loci is a function of phase and amplitude distortions due to phase/amplitude response coupling.
In addition to data encoding, it is also known to provide various analog electrical signal processing functions in order to modify the drive signals S(t). For example, U.S. Pat. No. 6,522,439 (Price et al.), U.S. Pat. No. 6,574,389 (Schemmann et al.), and U.S. Pat. No. 6,687,432 (Schemmann et al.) teach optical transmitters which compensate chromatic dispersion (or, more generally, odd order distortions) of an optical link by predistorting the drive signals. As shown in FIG. 2, these systems provide a signal distorter 14 between the driver circuit 10 and the E/O converter 4. Thus, the drive signal 10 (in any of baseband, coded, or modulated electrical carrier formats) is supplied to the signal distorter 14 which imposes a dispersive function F[ ] on the drive signal S(t). The resulting distorted drive signal F[S(t)] is then supplied to the E/O converter 4 to generate a predistorted optical communications signal for transmission through the link.
In each of the above-noted patents, the signal distorter 12 is provided by an analog filter circuit (not shown) having a group delay characteristic selected to counteract chromatic dispersion of the link. Multiple filter circuits may be cascaded to compensate some other distortions. For example, Schemmann et al. teach that the (typically squaring response) of an optical receiver can also be precompensated at the transmitter, by means of a suitable filter circuit within the signal distorter 12.
A common characteristic among all of the above-noted predistortion techniques is that analog filter circuits are used to distort an otherwise conventionally generated (and thus conventionally formatted) analog drive signal S(t). The premise is that distorting the drive signal S(t) will suitably distort the optical signal 8 in such a way as to offset distortions due to impairments of the optical link. While this approach is satisfactory for compensating linear distortions (such as chromatic dispersion, and receiver squaring effects) it cannot compensate non-linear impairments such as SPM and four-wave mixing. Quite apart from the limitations inherent to analog filter circuits, all of which are well known, compensation of non-linear distortions is complicated by the fact that all real electro-optical devices (i.e. lasers, E/O converters etc.) exhibit a response in both phase and amplitude to changes in drive voltage (or current). This coupling of phase and amplitude responses means, for example, that any change in drive signal voltage required to produce a desired change in the optical E-field amplitude also produces a transient phase change (chirp), and vise-versa. Further complicating this situation is that the overall system response, in terms of changes in the output optical E-field (amplitude and/or phase) due to changes in drive signal voltage (or current) tends to be highly non-linear. As a result, the prior art techniques for compensating linear distortions (such as chromatic dispersion) by applying a dispersive function F[ ] to the drive signals S(t) typically results in compounding the effects of system non-linearities.
Applicant's co-pending U.S. patent applications Ser. Nos. 10/262,944, filed Oct. 3, 2002; Ser. No. 10/307,466 filed Dec. 2, 2002; Ser. No. 10/405,236 filed Apr. 3, 2003; and Ser. No. 10/677,223, filed Oct. 3, 2003, the contents of all of which are hereby incorporated herein by reference, and International Patent Application No. PCT/CA03/01044 filed Jul. 11, 2003 describe techniques for compensating both linear and non-linear impairments in an optical link by using a multi-bit digital signal path to generate the drive signals S(t). Thus, a signal processor 16 receives the input data signal x(t) as an input, and uses a compensation function C[ ] to compute successive multi-bit In-phase and Quadrature values (EI(n) and EQ(n), respectively) representing successive loci of the end-point of a desired or target optical E-field vector. A linearizer 18 then uses the multi-bit (EI(n), EQ(n)) loci to synthesize a pair of multi-bit digital drive signals VR(n) and VL(n). The digital drive signals Vx(n), in which x is an index identifying the involved branch of the signal path, are then converted into analog (RF) signals by respective high speed multi-bit Digital-to-Analog Converters (DACs) 20, which are then amplified (and possibly band-pass filtered to remove out-of-band noise) to generate the drive signals Sx(t) supplied to an E/O converter 22. The digital drive signals Vx(n) are computed such that the drive signals Sx(t) supplied to the E/O converter 22 will yield an optical E-field EO(t) at the E/O converter output 24 that is a high-fidelity reproduction of the target E-field computed by the signal processor 16.
In general, the signal processor 16 is capable of implementing any desired mathematical function, which means that the compensation function C[ ] can be selected to compensate any desired signal impairments, including, but not limited to, dispersion, Self-Phase Modulation (SPM), Cross-Phase Modulation (XPM), four-wave mixing and polarization dependent effects (PDEs) such as polarization dependent loss. In addition, the compensation function C[ ] can be dynamically adjusted for changes in the optical properties of the link, and component drift due to aging. The inherent flexibility of the mathematical function implemented by the signal processor 16 also implies that the signal processor 16 can be placed into a “test” mode, and used to generate (EI(n), EQ(n)) loci of a desired optical E-field vector independently (or even in the absence) of an input data signal x(t).
The linearizer 18 can also implement any desired mathematical function, and thus can perform signal format conversion (i.e. from Cartesian to polar coordinates); compensate for non-linearities in the signal path between the linearizer 18 and the output 24 of the E/O converter 22; and perform various scaling and clipping operations to limit dynamic range requirements of electrical components downstream of the linearizer 18 (principally the DACs 20).
The resolution of each analog drive signal Sx(t) is governed by that of the DACs 20. In general, each DAC 20 has a resolution of M-bits, where M is an integer, which yields excursions of each analog drive signal Sx(t) between 2M discrete levels. It will be noted that M=1 represents a trivial case, in which each analog drive signal Sx(t) is a bi-state signal similar to that produced by the conventional driver circuits described above with reference to FIGS. 1 and 2. In applicant's co-pending U.S. patent applications Ser. Nos. 10/262,944, filed Oct. 3, 2002; Ser. No. 10/307,466 filed Dec. 2, 2002; Ser. No. 10/405,236 filed Apr. 3, 2003; and Ser. No. 10/677,223, filed Oct. 3, 2003, and International Patent Application No. PCT/CA03/01044 filed Jul. 11, 2003, M is greater than 4.
The E/O converter 22 will normally be provided as either nested MZ interferometers, or as a conventional dual branch MZ interferometer, as illustrated in FIG. 3. In this latter configuration, each branch of the MZ modulator is driven with a respective one of the analog drive signal Sx(t) so as to perform polar (i.e. phase and amplitude) modulation of the E-field of the optical carrier 6. This solution is particularly advantageous in that it enables arbitrary E-field modulation using readily available (and relatively low-cost) optical components.
Multi-bit digital generation of the drive signals Sx(t) in this manner enables the optical transmitter to synthesize any desired E-field waveform at the output 24 of the polar E/O converter 22. Because the linearizer 18 synthesizes the digital drive signals Vx(n) based on a model of the target optical E-field (as opposed to the data signal being transmitted), it is possible to derive a mathematical representation of the entire data path between the signal processor 16 and the E/O converter output 24, which enables phase and amplitude of the output E-field EO(t) to be independently controlled, even with significant coupling of phase and amplitude responses of the polar E/O converter 22. This is an operational feature which is simply not possible in prior art transmitters.
An implicit limitation of this technique is that accurate synthesis of a desired optical E-field waveform at the E/O converter output 24 is contingent upon satisfying a number of criteria, including (but not necessarily limited to):                the drive signals Sx(t) must be supplied to respective branches of the E/O converter 22 with substantially zero phase and amplitude error;        generation of the drive signals must take into account the known response of the E/O converter 22, as well as “component drift” due to changes in temperature, and aging; and        the E/O converter must be driven to an optimal bias point.        
In addition to the inherent phase/amplitude response coupling and non-linearity of real electro-optical components, satisfying these criteria is complicated by the fact that each of the devices in the signal paths traversed by the drive signals Sx(t) are subject to manufacturing variations, as well as component drift due to temperature, aging and (in some cases) mechanical stress. As a result, an exact match between the two signal paths is not practicable.
A known method for dynamically controlling an E/O converter 4 of the type described above with reference to FIGS. 1-3, is to implement one or more control loops using a dither signal inserted into the drive signal S(t). Typically, such a dither signal takes the form of a low frequency sinusoidal analog signal that is added to the drive signals S(t), and detected in the optical signal at some point downstream of the E/O converter 4. Differences (typically of amplitude) between the added and detected dither signals provide a direct indication of gain, from which other performance characteristics may be inferred. The frequency of the dither signal is typically selected to be low enough to avoid interference with data traversing the signal path, but high enough to avoid being attenuated by low-frequency cut-off.
However, these techniques assume that the drive signal Sx(t) is formatted to drive the amplitude (or phase) response of the E/O converter between two states, as described above with reference to FIGS. 1a-c. For various reasons, these conventional techniques become progressively less accurate as the number of states increases (as in, for example, quadrature phase modulation described above with reference to FIGS. 1d-e). In the extreme cases of the dispersion compensated drive signals, using either the dispersive function F[ ] of FIG. 2 or the high-resolution signals of FIGS. 3a-c, conventional control loop techniques cannot distinguish between output optical signal variations due to the dispersive or compensation functions F[ ], and C[ ], respectively, from those produced by the dither signal. Furthermore, the conventional control loop techniques fail entirely in a situation where the drive signals Sx(t) are formatted to simultaneously drive desired excursions of both the phase and amplitude response of the E/O converter 22, as in the embodiment of FIGS. 3a-c. 
Accordingly, methods and apparatus for cost-effectively controlling a polar optical transmitter to accurately synthesize a desired optical E-field waveform remains highly desirable.